Word Problems

Question

You have fallen down a slippery well 10 feet deep. Every hour you are able to climb 2 feet out of the well, but then slip down 1 foot. How many hours total will it take for you to climb out of the well?

Answer 1

note:  edited based on Mark M.'s comment.

 

To show the depth values:

 

elapsed

hours    feet at start of hour        height achieved    feet at end of hour

  0                10                                     8                             9

  1                  9                                     7                             8

  2                  8                                     6                             7

  3                  7                                     5                             6

  4                  6                                     4                             5

  5                  5                                     3                             4

  6                  4                                     2                             3

  7                  3                                     1                             2

  8                  2                                     0   <-- **get out before sliding down

  9                                                                   [no more wall to climb on]

 

9 hours after falling [not during the ninth hour], you may climb out.  [note that the question asks, "How many hours total will it take for you?" not "on which hour will you exit?"]

Answer 2

You climb out on hour nine - before you slip back one foot.

Answer 3

It looks like on average, you climb 1 ft per hour, accounting for 2 feet up minus 1 foot down each hour.  Then it would take 10 hours to climb 10 ft at an average rate of 1 ft per hour.

 

But as Mark pointed out, you reach 10 feet during the 9th hour, so you could escape the well during the 9th hour before you slide back a foot.  If you do slide back a foot during the 9th hour, then you will need an additional hour.